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Introduction

The analysis in this part is the same with PLIER-Canonical. But in this part, I used Adipose Subcutaneous expression data. It contains 581 samples.

Material and Methods

This part is the same with PLIER-Canonical.

Snps after filter

After filtering by ‘pval < 5e-8’ and LD Clumping, for each trait, I got :

platelet count trait contains 691 SNPs with pval<5e-8.

white blood cell count trait contains 367 SNPs with pval<5e-8.

myeloid white cell count trait contains 317 SNPs with pval<5e-8.

lymphocyte count trait contains 446 SNPs with pval<5e-8.

red blood cell count trait contains 462 SNPs with pval<5e-8.

granulocyte count trait contains 308 SNPs with pval<5e-8.

eosinophil count trait contains 496 SNPs with pval<5e-8.

neutrophil count trait contains 311 SNPs with pval<5e-8.

IBD trait contains 118 SNPs with pval<5e-8.

Ulcerative colitist trait contains 75 SNPs with pval<5e-8.

Crohn’s disease trait contains 97 SNPs with pval<5e-8.

BMI trait contains 102 SNPs with pval<5e-8.

T2D contains 14 SNPs with pval<5e-8. T2D_2 contains 4 SNPs with pval<5e-8.

Asthma trait contains 192 SNPs with pval<5e-8. Asthma_2 trait contains 110 SNPs with pval<5e-8.

HDL trait contains 225 SNPs with pval<5e-8.

LDL trait contains 203 SNPs with pval<5e-8.

WHR trait contains 37 SNPs with pval<5e-8.

Results - pval < 5e-8 & 120 PEER factors & covariants: 10 PCs + GTEx:Sequencing platform,Sequencing protocol,Sex + AGE

Summary table

I used ‘qvalue’ R package to compute the fdr from p-values for each SNP and made a table to show the number of SNPs that pass the threshold. The thresholds are ‘fdr < 0.1’,‘fdr < 0.2’,‘pval < 5e-8’. The ‘num_significant_pairs’ indicates the number of significant pairs under each threshold. If a trait~factor pair has as least 1 significant SNP, we named it as ‘significant pair’.

Info table

For each trait, I made a table to show the info of snps with fdr>0.2 in the factor ~ SNP + genotype pcs association test. For each trait,The LVs have more than one significant SNPs with FDR<0.2 are included.

The suffix ’_assoc’ here means that results are from factor ~ SNP + genotype pcs association test. The suffix ’_gwas’ here means results are from original GWAS results files. For EUR.CD, EUR.IBD, EUR.UC, the effectsize_gwas here means ‘ln(OR)’, for others, it means ‘beta’.

‘snp_ld’ here means the snps that in LD with the snp in each line.’ld_r2’ means the LD r-squared which is corresponding to the ‘snp_ld’ column. ‘cis-eqtl’ column indicates whether the snp is a cis-eqtl according to GTEx data. ‘cis_gene_hgnc’ and ‘cis_gene_hgnc’ is the genes that the snp influence when it act as cis-eqtl. ‘func’ and ‘func_gene’ are obtained from ANNOVAR, which indicating the snp function within the genes.

Enrichment analysis

Eocinophil/granulocyte count/neutrophil count/lymphocyte count/myeloid white cell count - LV74

Eocinophil - LV84

Eocinophil - LV121

Ulcerative colitist - LV29

LDL - LV35

Warning in instance$preRenderHook(instance): It seems your data is too big
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Red Blood Cell Count - LV104

Effect size plots

For each trait, I made a plot of association with LV(indicating by beta in GWAS) vs association with trait(indicating by ln(odds ratio) or beta in GWAS) to show if the variants have the correlated effect direction. The effect sizes of Catalog GWAS and factor association tests are harmonized by TwoSampleMR R package to make the effect alleles in these two analysis identical. The LVs have more than one significant SNPs with FDR<0.2 are included in the plotting.Besides, for each plots, I fitted the points with intercept = 0. The pvalues and r-squared are shown on the plots.

Asthma_2

None of the LVs have >1 SNPs at FDR<0.2.

BMI

Eosinophil count

Crohn’s disease

IBD

Ulcerative colitist

granulocyte count

HDL

None of the LVs have >1 SNPs at FDR<0.2.

LDL

lymphocyte count

myeloid white cell count

neutrophil count

plt

rbc

T2D_2

None of the LVs have >1 SNPs at FDR<0.2.

T2D

None of the LVs have >1 SNPs at FDR<0.2.

asthma

wbc

None of the LVs have >1 SNPs at FDR<0.2.

eo

None of the LVs have >1 SNPs at FDR<0.2.

Resampling

For some promising trait-factor pairs, I did resampling. I resampled the SNPs without replacement, I fitted the points with intercept = 0 again and recorded the pvalues and r-squared. The resampling was repeated 1000 times. The following plots are the resampling results.

I made a histogram to show the pvalues/rsquared distribution from resampling. The red line in the plots are the pvalue/rsquared in the origin analysis. The p_mean/r_mean values in the plots are the mean values of the resampling. The ‘prob of getting more extreme values’ is computed by: (number of more extreme values)/(times of resampling)

Eosinophil count

Ulcerative colitist

granulocyte count

LDL

lymphocyte count

neutrophil count

myeloid white cell count

red blood cell count

Effect size plots- more SNPs

For some promising trait-factor pairs , I relaxed the fdr threshold of the SNPs that used to make effect size plots(from 0.2 to 0.3/0.5)

Eosinophil count

Ulcerative colitist

granulocyte count

LDL

lymphocyte count

neutrophil count

myeloid white cell count

red blood cell count

Effect size plots - checking the reverse causality

To check if the effect size correlation is due to reverse causality: i.e. trait -> LV (trait causally affect LV), instead of LV -> trait (which is what we like to see). I used all SNPs associated with traits(pval<5E-8). The x-axis is the effects of these SNPs on trait, and y-axis is the effects on LV.

Some pair show p < 0.05, the result may be driven by the possible causal effect of LV -> trait. To test this, I removed the SNPs that are associated with LVs at FDR < 0.2 and made the plots again.

Eosinophil count

Ulcerative colitist

granulocyte count

LDL

lymphocyte count

neutrophil count

myeloid white cell count

red blood cell count

QQplots - promising pairs

Eosinophil count

Ulcerative colitist

granulocyte count

LDL

lymphocyte count

neutrophil count

myeloid white cell count

red blood cell count

Colocalization

The colocalization analysis was performed using the approximate Bayes factor test implemented in the Coloc package. Coloc computes five posterior probabilities (PP0, PP1, PP2, PP3 and PP4), each corresponding to a hypothesis: H0, no association with either trait; H1, association with trait 1 but not with trait 2; H2, association with trait 2 but not with trait 1; H3, association with trait 1 and trait 2, two independent SNPs; H4, association with trait 1 and trait 2, one shared SNP. We ran Coloc with the default parameters and used PP4 to assess evidence of colocalization. We visualized the colocalization of factor - QTLs and GWAS associations using the LocusCompareR package.

Chromosome selection: I first sorted the SNPs by their pvalues from factor association tests, then I selected the first two SNPs and chose their chromosome to do the colocalization test adn visualization.

Eosinophil count

LV74

pvalues in coloclization
note
nsnps 654 NA
PP.H0.abf 4.32951012214208e-15 no association with either trait
PP.H1.abf 1.47039883050559e-14 association with trait 1 but not with trait 2
PP.H2.abf 0.012147306446318 association with trait 2 but not with trait 1
PP.H3.abf 0.0403074343772307 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.947545259176435 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 551 NA
PP.H0.abf 4.51503740879928e-15 no association with either trait
PP.H1.abf 1.49802568801237e-14 association with trait 1 but not with trait 2
PP.H2.abf 0.0109205471062468 association with trait 2 but not with trait 1
PP.H3.abf 0.035279033577639 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.953800419316093 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 587 NA
PP.H0.abf 1.30154749414775e-21 no association with either trait
PP.H1.abf 9.73567901978272e-22 association with trait 1 but not with trait 2
PP.H2.abf 0.0301083403492439 association with trait 2 but not with trait 1
PP.H3.abf 0.0215729599148834 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.948318699735872 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 100 NA
PP.H0.abf 0.895363538820831 no association with either trait
PP.H1.abf 0.0964494552470313 association with trait 1 but not with trait 2
PP.H2.abf 0.00366956720683393 association with trait 2 but not with trait 1
PP.H3.abf 0.00039116317140931 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00412627555389428 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 151 NA
PP.H0.abf 0.909990082714903 no association with either trait
PP.H1.abf 0.0806086328367058 association with trait 1 but not with trait 2
PP.H2.abf 0.00549203403761318 association with trait 2 but not with trait 1
PP.H3.abf 0.000483068521375786 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00342618188940235 association with trait 1 and trait 2, one shared SNP

lv84

pvalues in coloclization
note
nsnps 633 NA
PP.H0.abf 0.520867968468262 no association with either trait
PP.H1.abf 0.219558425612122 association with trait 1 but not with trait 2
PP.H2.abf 0.0163221224603899 association with trait 2 but not with trait 1
PP.H3.abf 0.00664356080914982 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.236607922650077 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 670 NA
PP.H0.abf 9.52195421752099e-90 no association with either trait
PP.H1.abf 1.96819913996693e-90 association with trait 1 but not with trait 2
PP.H2.abf 0.693469246408423 association with trait 2 but not with trait 1
PP.H3.abf 0.143177555947148 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.163353197644415 association with trait 1 and trait 2, one shared SNP

lv121

pvalues in coloclization
note
nsnps 836 NA
PP.H0.abf 0.803428972151636 no association with either trait
PP.H1.abf 0.128323078245838 association with trait 1 but not with trait 2
PP.H2.abf 0.0528939231585165 association with trait 2 but not with trait 1
PP.H3.abf 0.00844126532987787 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00691276111413178 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 583 NA
PP.H0.abf 4.52990830876848e-06 no association with either trait
PP.H1.abf 9.21861694069134e-07 association with trait 1 but not with trait 2
PP.H2.abf 0.0916212125783412 association with trait 2 but not with trait 1
PP.H3.abf 0.0177548110256025 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.890618524626053 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 281 NA
PP.H0.abf 2.77707888116324e-29 no association with either trait
PP.H1.abf 2.10073251325066e-30 association with trait 1 but not with trait 2
PP.H2.abf 0.395264611924459 association with trait 2 but not with trait 1
PP.H3.abf 0.029324540040624 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.575410848034918 association with trait 1 and trait 2, one shared SNP

Ulcerative colitist

pvalues in coloclization
note
nsnps 466 NA
PP.H0.abf 6.36858252526649e-12 no association with either trait
PP.H1.abf 1.25749787143433e-12 association with trait 1 but not with trait 2
PP.H2.abf 0.76638668186091 association with trait 2 but not with trait 1
PP.H3.abf 0.151243237668553 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.0823700804629126 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 484 NA
PP.H0.abf 2.39875722879442e-07 no association with either trait
PP.H1.abf 1.58234762077974e-08 association with trait 1 but not with trait 2
PP.H2.abf 0.871084985071383 association with trait 2 but not with trait 1
PP.H3.abf 0.0573898654077472 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.0715248938216703 association with trait 1 and trait 2, one shared SNP

granulocyte count

lv74

pvalues in coloclization
note
nsnps 807 NA
PP.H0.abf 0.000243730196779536 no association with either trait
PP.H1.abf 0.000165248082383001 association with trait 1 but not with trait 2
PP.H2.abf 0.115588213386481 association with trait 2 but not with trait 1
PP.H3.abf 0.077561897771207 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.80644091056315 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 786 NA
PP.H0.abf 3.19604103017961e-12 no association with either trait
PP.H1.abf 1.03593792505706e-11 association with trait 1 but not with trait 2
PP.H2.abf 0.014003650916366 association with trait 2 but not with trait 1
PP.H3.abf 0.0444487115504494 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.94154763751963 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 510 NA
PP.H0.abf 1.82259340012189e-17 no association with either trait
PP.H1.abf 1.92483992741527e-17 association with trait 1 but not with trait 2
PP.H2.abf 0.0297496892787095 association with trait 2 but not with trait 1
PP.H3.abf 0.030478859686348 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.939771451034946 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 510 NA
PP.H0.abf 1.82259340012189e-17 no association with either trait
PP.H1.abf 1.92483992741527e-17 association with trait 1 but not with trait 2
PP.H2.abf 0.0297496892787095 association with trait 2 but not with trait 1
PP.H3.abf 0.030478859686348 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.939771451034946 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 172 NA
PP.H0.abf 1.69067886793852e-46 no association with either trait
PP.H1.abf 5.78786302442303e-48 association with trait 1 but not with trait 2
PP.H2.abf 0.249934649969975 association with trait 2 but not with trait 1
PP.H3.abf 0.00781400109211381 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.742251348937904 association with trait 1 and trait 2, one shared SNP

LDL

lv35

pvalues in coloclization
note
nsnps 150 NA
PP.H0.abf 1.14243004211355e-21 no association with either trait
PP.H1.abf 4.88169641330046e-23 association with trait 1 but not with trait 2
PP.H2.abf 0.914923549379037 association with trait 2 but not with trait 1
PP.H3.abf 0.039049399756932 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.04602705086403 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 80 NA
PP.H0.abf 2.38940663497786e-14 no association with either trait
PP.H1.abf 7.2663269498117e-15 association with trait 1 but not with trait 2
PP.H2.abf 0.594951780945732 association with trait 2 but not with trait 1
PP.H3.abf 0.180704012500906 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.224344206553332 association with trait 1 and trait 2, one shared SNP

lymphocyte count

lv74

pvalues in coloclization
note
nsnps 786 NA
PP.H0.abf 1.7445088448985e-35 no association with either trait
PP.H1.abf 5.65450460730246e-35 association with trait 1 but not with trait 2
PP.H2.abf 0.0120008783933029 association with trait 2 but not with trait 1
PP.H3.abf 0.0379485898305526 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.950050531776139 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 510 NA
PP.H0.abf 1.07493786039491e-42 no association with either trait
PP.H1.abf 1.13524130672266e-42 association with trait 1 but not with trait 2
PP.H2.abf 0.0295868451797152 association with trait 2 but not with trait 1
PP.H3.abf 0.030306544960568 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.940106609859711 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 56 NA
PP.H0.abf 3.43436637262214e-46 no association with either trait
PP.H1.abf 2.92432501543514e-47 association with trait 1 but not with trait 2
PP.H2.abf 0.0605874640743969 association with trait 2 but not with trait 1
PP.H3.abf 0.00422376684575926 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.935188769079843 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 151 NA
PP.H0.abf 0.909367744368301 no association with either trait
PP.H1.abf 0.0805535049356063 association with trait 1 but not with trait 2
PP.H2.abf 0.00659955289120895 association with trait 2 but not with trait 1
PP.H3.abf 0.000581703311602042 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00289749449328192 association with trait 1 and trait 2, one shared SNP

neutrophil count

pvalues in coloclization
note
nsnps 807 NA
PP.H0.abf 0.000214294779531181 no association with either trait
PP.H1.abf 0.000145290989176229 association with trait 1 but not with trait 2
PP.H2.abf 0.117951543823456 association with trait 2 but not with trait 1
PP.H3.abf 0.079168146384457 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.80252072402338 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 786 NA
PP.H0.abf 2.82528454381721e-09 no association with either trait
PP.H1.abf 9.15764028177483e-09 association with trait 1 but not with trait 2
PP.H2.abf 0.0153647114415028 association with trait 2 but not with trait 1
PP.H3.abf 0.048866117423375 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.935769159152199 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 510 NA
PP.H0.abf 1.44966591128561e-13 no association with either trait
PP.H1.abf 1.53099140338639e-13 association with trait 1 but not with trait 2
PP.H2.abf 0.0296802594352 association with trait 2 but not with trait 1
PP.H3.abf 0.0304053919677193 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.939914348596783 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 56 NA
PP.H0.abf 1.5259694149023e-14 no association with either trait
PP.H1.abf 1.29934609433665e-15 association with trait 1 but not with trait 2
PP.H2.abf 0.0596791572833565 association with trait 2 but not with trait 1
PP.H3.abf 0.00414543889146503 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.936175403825163 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 172 NA
PP.H0.abf 9.90493571701678e-41 no association with either trait
PP.H1.abf 3.39085158529905e-42 association with trait 1 but not with trait 2
PP.H2.abf 0.262118676406559 association with trait 2 but not with trait 1
PP.H3.abf 0.00824372229545226 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.729637601297983 association with trait 1 and trait 2, one shared SNP

myeloid white cell count

pvalues in coloclization
note
nsnps 807 NA
PP.H0.abf 0.000126242289634006 no association with either trait
PP.H1.abf 8.5591759056958e-05 association with trait 1 but not with trait 2
PP.H2.abf 0.112136433902647 association with trait 2 but not with trait 1
PP.H3.abf 0.0752156101050989 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.812436121943563 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 786 NA
PP.H0.abf 1.06923834059985e-14 no association with either trait
PP.H1.abf 3.46573944919043e-14 association with trait 1 but not with trait 2
PP.H2.abf 0.0134520292367394 association with trait 2 but not with trait 1
PP.H3.abf 0.0426583893747474 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.943889581388469 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 510 NA
PP.H0.abf 2.39167301496117e-20 no association with either trait
PP.H1.abf 2.52584460813423e-20 association with trait 1 but not with trait 2
PP.H2.abf 0.0296523673059772 association with trait 2 but not with trait 1
PP.H3.abf 0.0303758776983773 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.939971754995643 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 56 NA
PP.H0.abf 1.68997869196331e-22 no association with either trait
PP.H1.abf 1.43899818139885e-23 association with trait 1 but not with trait 2
PP.H2.abf 0.0589076369402022 association with trait 2 but not with trait 1
PP.H3.abf 0.00407890673429991 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.937013456325495 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 151 NA
PP.H0.abf 0.908607813893165 no association with either trait
PP.H1.abf 0.0804861888650081 association with trait 1 but not with trait 2
PP.H2.abf 0.00680067114563086 association with trait 2 but not with trait 1
PP.H3.abf 0.000598909823017954 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00350641627317808 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 740 NA
PP.H0.abf 0.696244518692255 no association with either trait
PP.H1.abf 0.241303199421013 association with trait 1 but not with trait 2
PP.H2.abf 0.0295609541707098 association with trait 2 but not with trait 1
PP.H3.abf 0.0102225146358729 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.0226688130801494 association with trait 1 and trait 2, one shared SNP

red blood cell count

pvalues in coloclization
note
nsnps 1 NA
PP.H0.abf 0.999890377109835 no association with either trait
PP.H1.abf 5.59464824756157e-05 association with trait 1 but not with trait 2
PP.H2.abf 5.08322124194453e-05 association with trait 2 but not with trait 1
PP.H3.abf 0 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 2.84419527022698e-06 association with trait 1 and trait 2, one shared SNP
pvalues in coloclization
note
nsnps 434 NA
PP.H0.abf 0.884468683582122 no association with either trait
PP.H1.abf 0.0929659932493666 association with trait 1 but not with trait 2
PP.H2.abf 0.0163931929316615 association with trait 2 but not with trait 1
PP.H3.abf 0.00171862555024174 association with trait 1 and trait 2,two independent SNPs
PP.H4.abf 0.00445350468660804 association with trait 1 and trait 2, one shared SNP

sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.5        rstudioapi_0.11   whisker_0.3-2     knitr_1.30       
 [5] magrittr_1.5      R6_2.4.1          rlang_0.4.8       highr_0.8        
 [9] stringr_1.4.0     tools_3.6.1       DT_0.15           xfun_0.18        
[13] git2r_0.26.1      crosstalk_1.1.0.1 htmltools_0.5.0   ellipsis_0.3.1   
[17] rprojroot_1.3-2   yaml_2.2.1        digest_0.6.25     tibble_3.0.3     
[21] lifecycle_0.2.0   crayon_1.3.4      later_1.1.0.1     htmlwidgets_1.5.2
[25] vctrs_0.3.4       promises_1.1.1    fs_1.5.0          glue_1.4.2       
[29] evaluate_0.14     rmarkdown_1.13    stringi_1.5.3     compiler_3.6.1   
[33] pillar_1.4.6      backports_1.1.10  jsonlite_1.7.1    httpuv_1.5.1     
[37] pkgconfig_2.0.3